

<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
  <meta charset="utf-8">
  
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  
  <title>3.4.1.5. QzSimple1 Material &mdash; OpenSees Documentation  documentation</title>
  

  
  
  
  

  
  <script type="text/javascript" src="../../../../_static/js/modernizr.min.js"></script>
  
    
      <script type="text/javascript" id="documentation_options" data-url_root="../../../../" src="../../../../_static/documentation_options.js"></script>
        <script type="text/javascript" src="../../../../_static/jquery.js"></script>
        <script type="text/javascript" src="../../../../_static/underscore.js"></script>
        <script type="text/javascript" src="../../../../_static/doctools.js"></script>
        <script type="text/javascript" src="../../../../_static/language_data.js"></script>
        <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
    
    <script type="text/javascript" src="../../../../_static/js/theme.js"></script>

    

  
  <link rel="stylesheet" href="../../../../_static/css/theme.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/css/custom.css" type="text/css" />
    <link rel="index" title="Index" href="../../../../genindex.html" />
    <link rel="search" title="Search" href="../../../../search.html" />
    <link rel="next" title="3.4.2. nDMaterial Command" href="../ndMaterial.html" />
    <link rel="prev" title="3.4.1.4. TzSimple1 Material" href="TzSimple1.html" /> 
</head>

<body class="wy-body-for-nav">

   
  <div class="wy-grid-for-nav">
    
    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
      <div class="wy-side-scroll">
        <div class="wy-side-nav-search" >
          

          
            <a href="../../../../index.html">
          

          
            
            <img src="../../../../_static/OpenSeesLogo.png" class="logo" alt="Logo"/>
          
          </a>

          
            
            
          

          
<div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../../search.html" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>

          
        </div>

        <div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
          
            
            
              
            
            
              <p class="caption"><span class="caption-text">Applications for Users</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../../interpreters.html">1. OpenSees Interpreters</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../install.html">2. Installation</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../../../userManual.html">3. Command Manual</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../../modelCommands.html">3.1. Modelling Commands</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../analysisCommands.html">3.2. Analysis Commands</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../outputCommands.html">3.3. Output Commands</a></li>
<li class="toctree-l2 current"><a class="reference internal" href="../../materialCommands.html">3.4. Material Commands</a><ul class="current">
<li class="toctree-l3 current"><a class="reference internal" href="../uniaxialMaterial.html">3.4.1. uniaxialMaterial Command</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="Steel01.html">3.4.1.1. Steel01 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="Steel02.html">3.4.1.2. Steel02 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="PySimple1.html">3.4.1.3. PySimple1 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="TzSimple1.html">3.4.1.4. TzSimple1 Material</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">3.4.1.5. QzSimple1 Material</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../ndMaterial.html">3.4.2. nDMaterial Command</a></li>
<li class="toctree-l3"><a class="reference internal" href="../section.html">3.4.3. section Command</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../miscCommands.html">3.5. Misc. Commands</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../../userExamples.html">4. Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../messageBoard.html">5. Questions, Bugs &amp; Feauture Requests</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/license.html">6. Copyright and License</a></li>
</ul>
<p class="caption"><span class="caption-text">Framework for Developer</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/sourceCode.html">1. Source Code</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/build.html">2. Building Application</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/references.html">3. References</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/extend.html">4. Extending Application</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/contribute.html">5. Contributing Code</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/issues.html">6. Issues</a></li>
</ul>

            
          
        </div>
      </div>
    </nav>

    <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">

      
      <nav class="wy-nav-top" aria-label="top navigation">
        
          <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
          <a href="../../../../index.html">OpenSees Documentation</a>
        
      </nav>


      <div class="wy-nav-content">
        
        <div class="rst-content">
        
          















<div role="navigation" aria-label="breadcrumbs navigation">

  <ul class="wy-breadcrumbs">
    
      <li><a href="../../../../index.html">Docs</a> &raquo;</li>
        
          <li><a href="../../../userManual.html"><span class="section-number">3. </span>Command Manual</a> &raquo;</li>
        
          <li><a href="../../materialCommands.html"><span class="section-number">3.4. </span>Material Commands</a> &raquo;</li>
        
          <li><a href="../uniaxialMaterial.html"><span class="section-number">3.4.1. </span>uniaxialMaterial Command</a> &raquo;</li>
        
      <li><span class="section-number">3.4.1.5. </span>QzSimple1 Material</li>
    
    
      <li class="wy-breadcrumbs-aside">
        
            
            <a href="../../../../_sources/user/manual/material/uniaxialMaterials/QzSimple1.rst.txt" rel="nofollow"> View page source</a>
          
        
      </li>
    
  </ul>

  
  <hr/>
</div>
          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
           <div itemprop="articleBody">
            
  <div class="section" id="qzsimple1-material">
<span id="qzsimple1"></span><h1><span class="section-number">3.4.1.5. </span>QzSimple1 Material<a class="headerlink" href="#qzsimple1-material" title="Permalink to this headline">¶</a></h1>
<p>This command is used to construct a QzSimple1 uniaxial material object:</p>
<dl class="function">
<dt>
<code class="sig-name descname">uniaxialMaterial QzSimple1 $matTag $qzType $qult $Z50 &lt;$suction $c&gt;</code></dt>
<dd></dd></dl>

<table class="colwidths-given docutils align-default">
<colgroup>
<col style="width: 17%" />
<col style="width: 17%" />
<col style="width: 67%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Argument</p></th>
<th class="head"><p>Type</p></th>
<th class="head"><p>Description</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>$matTag</p></td>
<td><p><em>integer</em></p></td>
<td><p>integer tag identifying material</p></td>
</tr>
<tr class="row-odd"><td><p>$qzType</p></td>
<td><p><em>integer</em></p></td>
<td><p>1 or 2 see note.</p></td>
</tr>
<tr class="row-even"><td><p>$qult</p></td>
<td><p><em>float</em></p></td>
<td><p>Ultimate capacity of the q-z material. SEE NOTE 1.</p></td>
</tr>
<tr class="row-odd"><td><p>$Z50</p></td>
<td><p><em>float</em></p></td>
<td><p>Displacement at which 50% of qult is mobilized in monotonic loading.</p></td>
</tr>
<tr class="row-even"><td><p>$suction</p></td>
<td><p><em>float</em></p></td>
<td><p>Uplift resistance is equal to suction*qult. Default = 0.0.</p></td>
</tr>
<tr class="row-odd"><td><p>$c</p></td>
<td><p><em>float</em></p></td>
<td><p>Viscous damping term (default = 0.0). see note</p></td>
</tr>
</tbody>
</table>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>qzType = 1 Backbone of q-z curve approximates Reese and O’Neill’s (1987) relation for drilled shafts in clay.</p>
<p>qzType = 2 Backbone of q-z curve approximates Vijayvergiya’s (1977) relation for piles in sand.</p>
<p>$qult: Ultimate capacity of the q-z material. Note that “q” or “qult” are stresses [force per unit area of pile tip] in common design equations, but are both loads for this uniaxialMaterial [i.e., stress times tip area].</p>
<p>$Y50: Displacement at which 50% of pult is mobilized in monotonic loading. Note that Vijayvergiya’s relation (qzType=2) refers to a “critical” displacement (zcrit) at which qult is fully mobilized, and that the corresponding z50 would be 0. 125zcrit.</p>
<p>$suction: The value of suction must be 0.0 to 0.1.*</p>
<p>$c: The viscous damping term (dashpot) on the far-field (elastic) component of the displacement rate (velocity). Nonzero c values are used to represent radiation damping effects.*</p>
<p>optional args $suction and $c must either both be omitted or both provided.</p>
</div>
<p>EQUATIONS and EXAMPLE RESPONSES:</p>
<p>The equations describing QzSimple1 behavior are similar to those for p-y materials by <a class="reference internal" href="#boulangeretal1999" id="id1"><span>[BoulangerEtAl1999]</span></a>. Modifications were required for representing the different responses of a &lt;math&gt;q-z` material in compression versus uplift.</p>
<p>The nonlinear q-z behavior is conceptualized as consisting of elastic (q-<span class="math notranslate nohighlight">\(z^e\)</span>), plastic (q-<span class="math notranslate nohighlight">\(z^p\)</span>), and gap (<span class="math notranslate nohighlight">\(q-z^g\)</span>) components in series. Radiation damping is modeled by a dashpot on the “far-field” elastic component (<span class="math notranslate nohighlight">\(q-z^e\)</span>) of the displacement rate. The gap component consists of a bilinear closure spring (<span class="math notranslate nohighlight">\(q^c-z^g\)</span>) in parallel with a nonlinear drag spring (<span class="math notranslate nohighlight">\(q^d-z^g\)</span>). Note that <span class="math notranslate nohighlight">\(z = z^e + z^p + z^g\)</span>, and that <span class="math notranslate nohighlight">\(q = q^d + q^c\)</span>.</p>
<p>The plastic component has an initial range of rigid behavior between <span class="math notranslate nohighlight">\(-C_r q_{ult} &lt; q &lt; C_r q_{ult}\)</span> with <span class="math notranslate nohighlight">\(C_r\)</span> = the ratio of <span class="math notranslate nohighlight">\(\frac{q}{q_{{ult}}}\)</span> when plastic yielding first occurs in virgin loading. The rigid range of q, which is initially <span class="math notranslate nohighlight">\(2 C_r q_{ult}\)</span>, translates and grows with plastic yielding. The rigid range of q is constrained to a maximum size of <span class="math notranslate nohighlight">\(0.7q_{{ult}}\)</span>. Beyond the rigid range, loading of the plastic (<span class="math notranslate nohighlight">\(q-z^p\)</span>) component is described by:</p>
<div class="math notranslate nohighlight">
\[q = q_{{ult}} - (q_{{ult}} - q_0) \left [\frac{c * z_{50}}{c * z_{50} + | z_p - z^p_0|} \right ]\]</div>
<p>where <span class="math notranslate nohighlight">\(q_ult\)</span> = the ultimate resistance of the <span class="math notranslate nohighlight">\(q-z\)</span> material in the current loading direction, <span class="math notranslate nohighlight">\(q_o = q\)</span> at the start of the current plastic loading cycle, p <span class="math notranslate nohighlight">\(z^p_o = z^p\)</span> at the start of the current plastic loading cycle, and c and n are constants that control the shape of <span class="math notranslate nohighlight">\(q-z^p\)</span> curve.</p>
<p>The closure (<span class="math notranslate nohighlight">\(q^c-z^g\)</span>) component is simply a bilinear elastic spring, which is relatively rigid in compression and extremely flexible in tension (uplift).</p>
<p>The nonlinear drag (<span class="math notranslate nohighlight">\(q^d-z^g\)</span>) component is used to allow thethe specification of some minimum “suction” on the pile tip during uplift. It is described by:</p>
<div class="math notranslate nohighlight">
\[q^d = C_d q_{ult} - (C_d q_{{ult}} - q^d_0) \left [\frac{z_{50}}{z_{50} + 2| z^g - z^g_0|} \right ]\]</div>
<p>where <span class="math notranslate nohighlight">\(C_d\)</span> = ratio of the maximum drag (suction) force to the ultimate resistance of the <span class="math notranslate nohighlight">\(q-z\)</span> material, <span class="math notranslate nohighlight">\(q^d_o = q^d\)</span> at the start of the current loading cycle, and <span class="math notranslate nohighlight">\(z^g_o = z^g\)</span> at the start of the current loading cycle.</p>
<p>The flexibility of the above equations can be used to approximate different q-z backbone relations. Reese and O’Neill’s (1987) recommended backbone for drilled shafts in clay is closely approximated using <span class="math notranslate nohighlight">\(c = 0.35\)</span>, <span class="math notranslate nohighlight">\(n = 1.2\)</span>, and <span class="math notranslate nohighlight">\(C_r = 0.2\)</span>. Vijayvergiya’s (1977) recommended backbone for piles in sand is closely approximated using <span class="math notranslate nohighlight">\(c = 12.3\)</span>, <span class="math notranslate nohighlight">\(n = 5.5\)</span>, and <span class="math notranslate nohighlight">\(C_r = 0.3\)</span>.</p>
<p>QzSimple1 is currently implemented to allow use of these two default sets of values. Values of <span class="math notranslate nohighlight">\(q_{ult}\)</span>, <span class="math notranslate nohighlight">\(z_50\)</span>, and suction (i.e., <span class="math notranslate nohighlight">\(C_d\)</span>) must then be specified to define the <span class="math notranslate nohighlight">\(q-z\)</span> material behavior.</p>
<p>Viscous damping on the far-field (elastic) component of the <span class="math notranslate nohighlight">\(q-z\)</span> material is included for approximating radiation damping. For implementation in OpenSees the viscous damper is placed across the entire material, but the viscous force is calculated as proportional to the component of velocity (or displacement) that developed in the far-field elastic component of the material. For example, this correctly causes the damper force to become zero during load increments across a fully formed gap in uplift. In addition, the total force across the <span class="math notranslate nohighlight">\(q-z\)</span> material is restricted to <span class="math notranslate nohighlight">\(q_{ult}\)</span> in magnitude so that the viscous damper cannot cause the total force to exceed the near-field soil capacity. Users should also be familiar with numerical oscillations that can develop in viscous damper forces under transient loading with certain solution algorithms and damping ratios. In general, an HHT algorithm is preferred over a Newmark algorithm for reducing such oscillations in materials like QzSimple1.</p>
<p>Examples of the monotonic backbones and cyclic loading response of QzSimple1 are given in the following plots.</p>
<div class="align-center figure">
<img alt="../../../../_images/QzSimple1A.gif" src="../../../../_images/QzSimple1A.gif" />
</div>
<div class="align-center figure">
<img alt="../../../../_images/QzSimple1B.gif" src="../../../../_images/QzSimple1B.gif" />
</div>
<div class="admonition-example admonition">
<p class="admonition-title">Example</p>
<p>The following constructs a PySimple material with tag <strong>101</strong>, soil type <strong>2</strong> (sand), <span class="math notranslate nohighlight">\(q_{ult}\)</span> of <strong>47216.4</strong> and a <span class="math notranslate nohighlight">\(Z_{50}\)</span> of <strong>0.00625</strong>. suction and c are set to <strong>0.0</strong>.</p>
<ol class="arabic simple">
<li><p><strong>Tcl Code</strong></p></li>
</ol>
<div class="highlight-tcl notranslate"><div class="highlight"><pre><span></span><span class="nv">uniaxialMaterial</span> QzSimple1 <span class="mi">101</span>  <span class="mi">2</span>  <span class="mf">47216.4</span>  <span class="mf">0.00625</span>  <span class="mf">0.0</span>  <span class="mf">0.0</span>
</pre></div>
</div>
<ol class="arabic simple" start="2">
<li><p><strong>Python Code</strong></p></li>
</ol>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">uniaxialMaterial</span><span class="p">(</span><span class="s1">&#39;QzSimple1&#39;</span><span class="p">,</span> <span class="mi">101</span><span class="p">,</span>  <span class="mi">2</span><span class="p">,</span>  <span class="mf">47216.4</span><span class="p">,</span>  <span class="mf">0.00625</span><span class="p">,</span>  <span class="mf">0.0</span><span class="p">,</span>  <span class="mf">0.0</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>Code Developed by: <a class="reference external" href="https://faculty.engineering.ucdavis.edu/boulanger/">Ross Boulanger</a>, UC Davis</p>
<dl class="citation">
<dt class="label" id="boulangeretal1999"><span class="brackets"><a class="fn-backref" href="#id1">BoulangerEtAl1999</a></span></dt>
<dd><p>Boulanger, R. W., Curras, C. J., Kutter, B. L., Wilson, D. W., and Abghari, A. (1999). “Seismic soil-pile-structure interaction experiments and analyses.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125(9): 750-759. Only minor changes have been made in its implementation for OpenSees.</p>
</dd>
</dl>
</div>


           </div>
           
          </div>
          <footer>
  

  <hr/>

  <div role="contentinfo">
    <p>
        &copy; Copyright 2020, The Regents of the University of California

    </p>
  </div>
  Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. 

</footer>

        </div>
      </div>

    </section>

  </div>
  


  <script type="text/javascript">
      jQuery(function () {
          SphinxRtdTheme.Navigation.enable(true);
      });
  </script>

  
  
    
    <!-- Theme Analytics -->
    <script>
    (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
      (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
      m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
    })(window,document,'script','https://www.google-analytics.com/analytics.js','ga');

    ga('create', 'UA-2431545-1', 'auto');
    ga('send', 'pageview');
    </script>

    
    

  <style>
         .wy-nav-content { max-width: none; }
  </style>



</body>
</html>